U.S. patent number 6,625,308 [Application Number 09/393,017] was granted by the patent office on 2003-09-23 for fuzzy distinction based thresholding technique for image segmentation.
This patent grant is currently assigned to Intel Corporation. Invention is credited to Tinku Acharya, A. K. V. Subba Rao, Ajay K. Ray.
United States Patent |
6,625,308 |
Acharya , et al. |
September 23, 2003 |
**Please see images for:
( Certificate of Correction ) ** |
Fuzzy distinction based thresholding technique for image
segmentation
Abstract
Embodiments of a fuzzy distinction based thresholding technique
for image segmentation are disclosed. In one embodiment, at least
one signal value level of the image is determined along which to
divide a fuzzy histogram, the histogram being based, at least in
part, on the image. The signal value represents a value which
produces a divided fuzzy histogram with an extreme value of one of
distinctiveness and fuzziness based on a measure of
multidimensional distance between measurement distributions and
their respective complements. The image is then segmented using the
at least one signal value.
Inventors: |
Acharya; Tinku (Chandler,
AZ), Ray; Ajay K. (West Bengal, IN), Rao; A. K. V.
Subba (West Bengal, IN) |
Assignee: |
Intel Corporation (Santa Clara,
CA)
|
Family
ID: |
28042113 |
Appl.
No.: |
09/393,017 |
Filed: |
September 10, 1999 |
Current U.S.
Class: |
382/168; 382/164;
382/170; 382/171; 706/8; 706/900 |
Current CPC
Class: |
G06K
9/38 (20130101); G06T 7/11 (20170101); G06T
7/143 (20170101); G06T 7/136 (20170101); G06T
2207/10016 (20130101); Y10S 706/90 (20130101) |
Current International
Class: |
G06K
9/38 (20060101); G06T 5/00 (20060101); G06K
009/00 (); G06K 009/34 (); G06G 007/00 () |
Field of
Search: |
;382/162,164,168,170,171
;706/8,14,900 |
References Cited
[Referenced By]
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46-49..
|
Primary Examiner: Johns; Andrew W.
Assistant Examiner: Alavi; Amir
Attorney, Agent or Firm: Wong; Sharon
Parent Case Text
RELATED APPLICATION
This patent application is related to concurrently filed U.S.
patent application Ser. No. 09/393,136, entitled, "A FUZZY BASED
THRESHOLDING TECHNIQUE FOR IMAGE SEGMENTATION," by Acharya et al.,
filed on Sep. 10, 1999, assigned to the assignee of the current
invention and herein incorporated by reference.
Claims
What is claimed is:
1. A method of segmenting a image comprising: determining at least
one signal value level of the potential signal value levels of the
image along which to divide a fuzzy histogram into at least two
measurement distributions, the histogram being based, at least in
part, on the image, the at least one signal value level being the
at least one of the potential signal value levels that produces a
divided fuzzy histogram having, based on a measure of the
multidimensional distance between each of the measurement
distributions and their respective complements, an extreme value of
one of distinctiveness and fuzziness; and segmenting the image
using the at least one signal value level.
2. The method of claim 1, wherein the image comprises a digital
image having digital pixel signal value levels at each pixel
location of the digital image.
3. The method of claim 2, wherein the digital pixel signal values
each comprise a plurality of bits.
4. The method of claim 3, wherein the plurality of bits comprises
eight bits.
5. The method of claims 3, wherein the digital image comprises a
gray scale digital image and the digital signal pixel value levels
of the digital image comprise gray scale digital signal value
levels.
6. The method of claim 3, wherein the digital image comprises a
color digital image, and wherein the color space format of the
color digital image comprises a three-color plane color space
format.
7. The method of claim 6, wherein determining the digital pixel
signal value level comprises determining the digital pixel signal
value level based, at least in part, on all three color space
planes of the digital image.
8. The method of claim 7, wherein segmenting the digital image
comprises segmenting all three color space planes of the digital
image.
9. The method of claim 6, wherein determining the digital pixel
signal value level comprises determining the digital pixel signal
value level based, at least in part, on at least any one of the
color space planes of the digital image.
10. The method of claim 9, wherein segmenting the digital image
comprises segmenting all three color-space planes of the digital
image.
11. The method of claim 9, wherein determining the digital pixel
signal value level comprises determining the digital pixel signal
value level based, at least in part, on only one of the color space
planes of the digital image.
12. The method of claim 11, wherein segmenting the digital image
comprises segmenting all three color space planes of the digital
image.
13. The method of claim 3, wherein the color space format of the
color digital image comprises the YUV color space format.
14. The method of claim 3, wherein the color space format of the
color digital image comprises the RGB color space format.
15. The method of claim 3, wherein determining the at least one
digital pixel signal value along which to divide the fuzzy
histogram comprises determining more than one digital pixel signal
value along which to divide the fuzzy histogram.
16. The method of claim 15, wherein determining more than one
digital pixel signal value along which to divide the fuzzy
histogram comprises determining two digital pixel signal values
along which to divide the fuzzy histogram.
17. The method of claim 15, wherein determining more than one
digital pixel signal value along which to divide the fuzzy
histogram comprises determining three digital pixel signal values
along which to divide the fuzzy histogram.
18. The method of claim 3, and further comprising: determining at
least one digital pixel signal value level along which to divide
another fuzzy histogram, the another fuzzy histogram being based,
at least in part, on one of the segmented portions of the digital
image, the at least one digital pixel signal value level of the
another fuzzy histogram being the at least one of the potential
digital pixel signal value levels of the digital image that
produces a divided another fuzzy histogram having the largest
distinctiveness based on a measure of the multidimensional distance
between each of the measurement distributions and their respective
complements; and segmenting the one of the segmented portions of
the digital image using the at least one digital pixel signal value
level.
19. The method of claim 1, wherein the at least one level of the
potential signal values produces a divided fuzzy histogram having
the greatest distinctiveness.
20. A method of segmenting an image comprising: constructing a
fuzzy histogram based, at least in part, on the signal value levels
of the image, wherein the fuzzy histogram is divided into at least
two measurement distributions along at least one of the potential
signal value levels of the image; computing one of the
distinctiveness and the fuzziness for the divided fuzzy histogram
using a measure of the multidimensional distance between each of
the measurement distributions and their respective complements;
repeating the prior two operations, constructing and computing, for
every potential signal value level of the image; determining the at
least one signal value level of the potential signal value levels
that provides the divided fuzzy histogram with an extreme value of
one of the distinctiveness and the fuzziness; and segmenting the
image using the at least one signal value level.
21. The method of claim 20, wherein the image comprises a digital
image having digital pixel signal value levels at each pixel
location of the digital image.
22. The method of claim 21, wherein the digital pixel signal values
each comprise a plurality of bits.
23. The method of claim 22, and further comprising: determining at
least one digital pixel signal value level along which to divide
another fuzzy histogram, the another fuzzy histogram being based,
at least in part, on one of the segmented portions of the digital
image, the at least one digital pixel signal value level of the
another fuzzy histogram being the at least one of the potential
digital pixel signal value levels of the digital image that
produces a divided another fuzzy histogram having the largest
distinctiveness based on a measure of multidimensional distance
between each measurement distribution and its respective
complement; and segmenting the one of the segmented portions of the
digital image using the at least one digital pixel signal value
level.
24. An apparatus comprising: a computing platform, said computing
platform being adapted to segment an image; said computing platform
further including the capability to: determine at least one signal
value level of the potential signal value levels of the image along
which to divide a fuzzy histogram, the fuzzy histogram being based,
at least in part, on the image, to produce a divided fuzzy
histogram, the at least one signal value level being the at least
one of the potential signal value levels that produces a divided
fuzzy histogram having the largest distinctiveness based on a
measure of multidimensional distance; and segment the image using
the at least one signal value level.
25. The apparatus of claim 24, wherein said computing platform
comprises at least one of a desktop personal computer, a laptop
personal computer, and a server.
26. The apparatus of claim 24, wherein said computing platform is
further adapted to segment a digital image having digital pixel
signal value levels in each pixel location of the digital
image.
27. The apparatus of claim 25, wherein the digital pixel signal
values of the digital image each comprise a plurality of bits.
28. An article comprising: a storage medium having stored thereon
instructions that, when executed by a computing platform, result in
the following operations by the computing platform to segment an
image: determining at least one signal value level of the potential
signal value levels of the image along which to divide a fuzzy
histogram, the fuzzy histogram being based, at least in part, on
the image, to produce a divided fuzzy histogram, the at least one
signal value level being the at least one of the potential signal
value levels that produces a divided fuzzy histogram having an
extreme based on a measure of multidimensional distance; and
segmenting the image using the at least one signal value level.
29. The article of claim 28, wherein said storage medium has stored
thereon instructions that, when executed, further result in the
computing platform segmenting a digital image having digital pixel
signal value levels in each pixel location of the digital
image.
30. The article of claim 29, wherein the digital pixel signal
values of the digital image each comprise a plurality of bits.
Description
BACKGROUND
Field
This disclosure is related to image processing, and, more
particularly, to image segmentation.
Background Information
As is well-known, image segmentation, in particular, image
segmentation of a digital image, has a variety of applications. For
example, such approaches may be employed in target tracking and
acquisition, navigation systems, recognition systems, video
conferencing, robotic vision, etc. These are just a few examples of
the types of applications in which image segmentation may be
employed. For example, an image may be segmented to be stored more
efficiently or to be transmitted across a communications system
having scalable bandwidth capabilities and so forth. Nonetheless,
image segmentation faces a number of challenges.
One such challenge is segmenting the image where the image content
may be blurred, rather than sharp. It is generally easier to
segment a sharp image than a blurred image. Another challenge in
segmenting an image arises where a histogram of signal values is
created based upon the content of the image and that histogram
contains discontinuities. Known techniques for segmenting an image
do not perform well, typically, in such circumstances. A need,
therefore, exists for a method or technique of segmenting an image
that addresses these foregoing challenges.
SUMMARY
Briefly, in accordance with one embodiment of the invention, a
method of segmenting an image includes the following. At least one
signal value level is determined, of the potential signal values of
the image, along which to divide a fuzzy histogram into at least
two measurement distributions, the histogram being based, at least
in part, on the image. The at least one signal value level is the
at least one of the potential signal value levels of the image that
produces a divided fuzzy histogram having, based on a measure of
the multidimensional distance between each of the measurement
distributions and their respective complements, an extreme value of
one of distinctiveness and fuzziness. The image is segmented using
the at least one signal value level.
Briefly, in accordance with another embodiment of the invention, a
method of segmenting an image includes the following. A fuzzy
histogram is constructed based, at least in part, on the signal
values levels of the image. The fuzzy histogram is divided into at
least two measurement distributions along at least one of the
potential signal value levels of the image to produce a divided
fuzzy histogram. One of the distinctiveness and the fuzziness for
the divided fuzzy histogram is computed using a measure of the
multidimensional distance between each of the measurement
distributions and their respective complements. The prior
operations are repeated for every potential signal value level of
the image. The at least one signal value level of the potential
signal value levels that provides the divided fuzzy histogram with
an extreme value of one of the distinctiveness and the fuzziness is
determined. The image is segmented using the at least one signal
value level.
Briefly, in accordance with yet another embodiment of the
invention, an article includes: a storage medium having stored
thereon instructions that, when executed by a computing platform,
result in the following operations by the computing platform to
segment an image. At least one signal value level of the potential
signal value levels of the image along which to divide a fuzzy
histogram is determined, the fuzzy histogram being based, at least
in part, on the image, the at least one signal value level being
the at least one of the potential signal value levels that produces
a divided fuzzy histogram having an extreme based on a measure of
multidimensional distance. The image is segmented image using the
at least one signal value level.
BRIEF DESCRIPTION OF THE DRAWINGS
The subject matter regarded as the invention is particularly
pointed out and distinctly claimed in the concluding portion of the
specification. The invention, however, both as to organization, and
method of operation, together with objects, features, and
advantages thereof, may best be understood by reference to the
following detailed description, when read with the accompanying
drawings in which:
FIG. 1 is a flowchart illustrating an embodiment of a method of
segmenting an image in accordance with the present invention;
FIG. 2 is a schematic diagram illustrating a five pixel-by-five
pixel digital image to which the embodiment of FIG. 1 may be
applied;
FIG. 3 is a plot of "crisp" histogram and a "fuzzy" histogram
produced by applying the embodiment of FIG. 1 to the digital image
of FIG. 2;
FIG. 4 is a schematic diagram illustrating segmented portions of
the digital image of FIG. 2 obtained after applying the embodiment
of FIG. 1;
FIG. 5 is a set of equations illustrating a calculation of
"distance" between each measurement distribution and its respective
complement in accordance with the embodiment of FIG. 1 for the
divided fuzzy histogram that provides the greatest distinctiveness
for the digital image of FIG. 2; and
FIG. 6 is a plot illustrating a typical shape of a membership
distribution that may be employed to characterize a "fuzzy
number."
DETAILED DESCRIPTION
In the following detailed description, numerous specific details
are set forth in order to provide a thorough understanding of the
invention. However, it will be understood by those skilled in the
art that the present invention may be practiced without these
specific details. In other instances, well-known methods,
procedures, components and circuits have not been described in
detail so as not to obscure the present invention.
As shall become more clear, an embodiment in accordance with the
present invention relates to image processing, such as digital
image processing. It is noted that, where digital image processing
is involved, the invention is not limited in scope to a digital
image of any particular dimensions. Likewise, the signal values or
pixel signal values in particular pixel locations are not
restricted in format or size. For example, although the invention
is not limited in scope in this respect, an eight bit binary
digital signal may be employed to represent the signal value in
each pixel location; however, alternatively, for example, analog,
rather than digital, signal values may be employed. Similarly,
although a digital image, for example, may comprise a rectangle
having the dimensions M pixels by N pixels, where M and N are
positive integers, of course, the invention is not limited to a
digital image of this particular shape. Nonetheless, a typical
format employed in this context comprises the common interchange
format (CIF) comprising 352 pixels by 288 pixels, although the
invention is not limited in scope in this respect. Likewise, the
image is not restricted in scope to employing either color or gray
scale pixel signal values. Likewise, if color is employed, any one
of a number of color space formats may be employed, such as the YUV
or RGB color space format.
As previously indicated, image processing, such as for digital
images, has a number of challenges. In particular, it is not clear
how to approach segmenting a digital image, for example, where
significant amounts of blurring are present in the image. Likewise,
it is not clear how to segment an image where discontinuities exist
in a histogram constructed representing the occurrence or frequency
of pixel signal values in the digital image. This means, for
example, that some signal value levels that are potential signal
value levels for the image are, nonetheless, not present in the
digital image, for example, at all. In this context, a "crisp"
histogram refers to a histogram that provides the frequency of
occurrence of all the potential pixel signal value levels of the
image, including those pixel signal value levels which, for that
particular pixel signal value level, have a zero frequency of
occurrence or magnitude. Throughout this detailed description, the
term "histogram" when used by itself refers to a "crisp" histogram
as just described. For images that include sharp edges, typically,
image segmentation is applied in the vicinity of such edges.
However, for segmentation of an image that is blurred or includes
blurring, it is frequently difficult to resolve or rely on such
edges. Since images are 2D projections of 3D world, information is
lost and thereby some uncertainty is introduced in the description
of the images. This uncertainty may be manifested in the
variability of pixel gray levels in an image, for example. Many
prominent image definitions, including the boundary between image
regions, contrast, etc. are essentially vague and, thus, fuzzy
notions may assist with characterization. The management of this
uncertainty in the pixel classification remains a useful
application area in image processing. In conventional literature on
segmentation, one idea has at time been overlooked and that is, the
segmented regions need not be mutually exclusive. It may be useful
to focus on how closely the segmented description can reproduce the
characteristics of the region. A possible approach includes
defining fuzzy regions characterized by a continuous gradation of
membership in it. Several techniques have been proposed in the
literature on the application of fuzzy set theory in image
segmentation, such as in S. K. Pal and N. R. Pal, "Segmentation
based on measures of contrast homogeneity and region size," IEEE
Trans System, Man and Cybernetics, 17, pp 857-868 (1987), and in,
S. K. Pal and A. Rosenfield, "Image enhancement and thresholding by
optimization of fuzzy compactness", Pattern Recognition, Vol. 7, pp
77-86 (1988). Some of the works include thresholding techniques
which reduce, typically to an extreme, the fuzziness in pixel
classification. Clustering techniques were also reported for image
segmentation based on Fuzzy c-means, as in, J. C. Bezdek, Pattern
Recognition using fuzzy objective function algorothms, Plenum
Press, New York (1981). Such approaches have been used for
segmentation of textured images, see H. H. Nguyen and P. Cohen,
"Gibbs random field, fuzzy clustering and the unsupervised
segmentation of textured images," CVGIP: Graphic Models & Image
Processing, Vol 55, pp 1-19 (1993), and also for segmentation of
remotely sensed aerial Scenes, M. Trivedi and J. C. Bezdek, "Low
level segmentation of aerial images with fuzzy clustering," IEEE
Trans System, Man and Cybernetics, Vol16, pp 341-359 (1986).
In a digital image, it is possible to have a reasonable number of
pixels with, for example, gray values (n-1) as well as (n+1), where
n is an integer, without the presence in the image of any pixels
with a gray value of n. However, typically, this does not affect
human visual response to the image. More particularly, the digital
image would not look perceptively different, if, in fact, instead
of (n+1) or (n-1), a gray value of n were present in the image.
This effect suggests that, for a digital image, gray values or
pixel signal value levels may be treated as "fuzzy numbers" which
are, in theory, normally convex sets on the real line. As shall be
described in more detail hereinafter, this approach may, therefore,
be employed to construct a "fuzzy histogram."In the case of a
"crisp" histogram, the frequency of occurrence of a particular gray
value does not affect the occurrence of other gray values. In other
words, the occurrences are independent events. However, in the case
of a fuzzy histogram, a gray value with more ambiguity may
contribute to the frequency of occurrence of nearby gray values
according to a membership assignment method. Thus, the frequency of
occurrence of gray values, for example, may be characterized as
"around n" for a fuzzy histogram. Symmetrical or asymmetrical fuzzy
numbers are employed to represent the notion of a gray level
"around n." A symmetrical fuzzy number may be characterized by a
membership distribution
where .alpha. controls the spread of the triangle and the function
f(.) controls the shape of the fuzzy number. Although the invention
is not limited in scope in this respect, a typical shape of a
triangular fuzzy number which is symmetrical is shown in FIG. 6 and
is given by
Therefore, in this context, a fuzzy histogram of a digital image is
a sequence of real numbers with S.sub.n representing the frequency
of occurrence of digital pixel signal values that are "around n."
Note that the sequence and n may be continuous in some situations,
in which case, the fuzzy histogram may be referred to as a fuzzy
distribution, although, for convenience, the term fuzzy histogram
will be used throughout this specification with no loss of
generality.
Here, let U.sub.A (X) designate the membership function of the
fuzzy set A with X being an element of X, where X is finite. If the
measure of fuzziness of the fuzzy set A, as described in H. J.
Zimmermann, Fuzzy Set Theory and its Applications, 2d edition,
Kluwer Academic Publishers, London, is denoted d(A), then this
measure may desirably exhibit the following properties: 1. d(A)
equals zero if A is a crisp set in X. 2. d(A) assumes a unique
maximum if U.sub.A (X) equals 0.5, for all x that is an element of
X. 3. d(A) is greater than or equal to d(A*), if A* is "crisper"
than A, ie, U.sub.A *(X) is less than or equal to U.sub.A (X), for
U.sub.A (X) less than or equal to 0.5, and, U.sub.A *(X) is greater
than or equal to U.sub.A (X), for U.sub.A (X) greater than or equal
to 0.5. 4. d(not-A) equals d(A), where "not-A" designates the
complement of A.
It is noted that although the membership function here is described
in terms of fuzziness, alternatively, it could be described in
terms of distinctiveness with similar properties because there is a
well-defined relationship between distinctiveness and fuzziness in
this context.
A potential measure of fuzziness comes from considering that for A
being a fuzzy set in X and A being its complement, then in contrast
to crisp sets, it is not necessarily true that
This means that fuzzy sets do not always satisfy the law of the
excluded middle, which is one of their major distinctions from
traditional crisp sets. It has been suggest elsewhere an approach
to measuring fuzziness is to view the fuzziness of a set in terms
of lack of distinction between the set and its complement. The less
a set differs from its complement the fuzzier it is. As a possible
metric to measure the distance between a fuzzy set and its
complement, Yager, for example, has suggested
.mu..sub. A (X)=1-.mu..sub.A (X) (classical fuzzy complement).
A measure of fuzziness of A can then be defined as
where, here, sup(A) indicates the elements which are contained in
the set A. Equation [3] suggests that measure of fuzziness may vary
between 0 and 1. This measure also satisfies properties 1 to 4
above.
This metric may also be consider a measure of the distance, in a
multidimensional sense, between a set and its complement, and, in
this context, becomes a fuzziness measure for the set. The term
"multidimensional" is used to recognize the potential values for
the parameter of p, although, as indicated above, and in the
context of the invention, one of those values may also be 1, i.e.,
the term multidimensional in this context includes a single
dimension. Likewise, it is noted that for a value of p equal to 1,
the multidimensional distance between a set and its complement
becomes the Hamming metric, and for a value of p equal to 2, the
multidimensional distance between a set and its complement becomes
the euclidean distance.
FIG. 1 is a flowchart illustrating an embodiment of a method of
segmenting an image, such as a digital image, in accordance with
the present invention that employs a measure of fuzziness based on
the multidimensional distance between a set and its complement, as
discussed above. In this approach, a pixel signal value level is
determined along which to divide a fuzzy histogram. The fuzzy
histogram is based, at least in part, on the image to be segmented.
In this embodiment, the determined pixel signal value level is the
pixel signal value level of the potential pixel signal value levels
that produces a segmented characterization, by dividing the fuzzy
histogram into at least two measurement distributions, having a
measure of fuzziness, based on a calculation of the
multidimensional distance between each of the measurement
distributions and their respective complements, that is an extreme
value. As one example, the fuzziness measurement may not be less
than the fuzziness measurement of any other divided fuzzy
histograms that are divided into distributions at other potential
pixel signal values. Of course, the invention is not limited in
scope to this particular embodiment. For example, in alternative
embodiments, more than two measurement distributions may be
employed. Likewise, an extreme value of the relevant parameter may
be used successfully, in accordance with the particular context.
For example, in equation [2] above, in an alternative embodiment,
the minus sign may be added. Therefore, employing the greatest or
least may depend on the context or situation. Further, in this
embodiment, as described in more detail hereinafter, the digital
image is then segmented using the determined signal value
level.
Initially, at 110 in FIG. 1, a fuzzy histogram, or its equivalent,
is constructed based, at least in part, on the image, in this
example, a digital image. This is accomplished by producing a fuzzy
histogram of all possible pixel signal value levels of the digital
image and, for each pixel signal value level, the fuzzy histogram
is calculated in this embodiment in accordance with equation [1],
although, of course, the invention is not limited in scope in this
respect. Any one of a number of distributions for characterizing a
"fuzzy number" may be employed to construct a fuzzy histogram and
provide satisfactory results and the invention is, therefore, not
restricted in scope to any particular one. To illustrate the
calculation, for a digital image in which the pixel signal values
comprise eight bits, the "bins" of the histogram, or potential
pixel signal value levels, include 0 to 255. Then, using this
histogram, multidimensional distance between each respective
measurement distribution and its complement, according to equation
[2] above, is calculated. To calculate multidimensional distance in
this particular embodiment, the fuzzy histogram is divided into at
least two membership distributions along at least one of the
potential pixel signal value levels of the digital image. For
example, assume that a particular pixel signal value level is the
s.sup.th signal value, eg, in this embodiment, "0" is the 1.sup.st,
"1" is the 2.sup.nd, etc. Then, at 120, the multidimensional
distance is computed for a membership distribution of the 1.sup.st
to s.sup.th pixel signal value levels and then, separately, the
multidimensional is computed for a membership distribution of the
(s+1).sup.th to n.sup.th pixel signal value levels. In this
embodiment, these operations or calculations are then repeated for
every potential signal value level of the digital image. More
specifically, via a loop formed by 130, 140, 150, 160 and 120, the
fuzzy histogram is divided into at least two membership
distributions along another at least one potential pixel signal
value level, but the level is different than a previous at least
one pixel signal value level for which this calculation has already
been performed. Then, at 130 again, the distinctiveness for this
divided fuzzy histogram is computed based on multidimensional
distance, as previously described. As indicated previously, the
construction of the divided fuzzy histogram and computation of its
fuzziness is repeated for every potential pixel signal value level,
from the 1.sup.st to n.sup.th, in this embodiment. Once this has
been accomplished, at 170, in this embodiment, it is determined
which potential pixel signal value level provides the divided fuzzy
histogram (or divided fuzzy histograms) having a calculated measure
of fuzziness that is the extreme. More specifically, for each
potential pixel signal value level, in this embodiment, the
multidimensional distance from respective complements for the at
least two membership distributions is summed and the sum is
employed as a measure of the distinctiveness of that particular
fuzzy histogram. Thus, at 170, the pixel signal value level that
provides the distinctiveness, over the potential pixel signal value
levels, not exceeded by any other is the pixel signal value level
that is used to segment the digital image. Where more than one
level results, such as because the same value results, either level
may be employed, of course.
Segmentation may be accomplished a variety of ways, depending, for
example, on the particular application, and the invention is not
limited in scope to a particular approach. For example, all the
pixel locations having a pixel signal value exceeding the
determined or threshold pixel signal value level may be included in
one image or frame in a video sequence of image frames, and those
locations where the pixel signal value does not exceed this level
may be considered as an object and this may be included in the
image frame. Likewise, the reverse may be done in a second frame or
image, eg, omitting those pixel signal values that exceed the
determined or threshold level and including the pixel signal values
for those locations where the pixel signal value level does not
exceed the determined level.
A sample application of this particular embodiment is illustrated
in FIGS. 2 and 3. This is, of course, provided merely for purposes
of illustration and is not intended to be limiting in any respect.
FIG. 2 is a diagram illustrating a five pixel-by-five pixel digital
image. In this particular embodiment, the pixel signal values each
comprise three bits. Therefore, the pixel signal value levels are
from 0 to 7 in this example. FIG. 3 is a plot illustrating the
"crisp" histogram constructed from this digital image. In this
simple example, by inspection of the histogram in FIG. 3, it might
be deduced that the pixel signal value level that produces the
greatest distinctiveness is pixel signal value level 4 or 5. The
multidimensional distance or distinctiveness calculation using
equation [2], illustrated in FIG. 5 for the two membership
distributions formed, confirms this. Of course, for a digital image
with hundreds of pixel signal value levels, and thousands of
pixels, making this determination is more challenging, and the
approach of this particular embodiment may be advantageously
employed. Furthermore, once the image has been segmented, such as
in accordance with the embodiment previously described, for
example, then this approach may be applied to the segmented
portions of the image to further segment those segmented
portions
Of course, a variety of segmentation approaches may be employed for
color images. For example, where the color space format of the
image comprises a three-color plane color space format, such as the
YUV color space format of the RGB color space format, a variety of
techniques may be employed, although the invention is not limited
in scope to these techniques or to employing color images or
three-color plane color space formats. Nonetheless, in one
embodiment, a fuzzy histogram may be produced for each color space,
and the pixel signal value employed may be based, at least in part,
on all three. Likewise, the color image may be segmented by
segmenting all three color space planes of the image.
Alternatively, a fuzzy histogram may be produced for any one of the
color space planes or for only a selected one of the color space
planes, and, again, all three color space plane images of the color
image may be segmented. Of course, additional variations are also
possible and within the scope of the present invention.
Alternatively, an image may be represented in YUV color space
format where the Y component contains luminance signal information
about the image. Thus, the previously described embodiment may be
applied to the Y component of the image to produce a segmented
characterization of the color image.
In this particular embodiment, where multidimensional distance
between each of the measurement distributions and their respective
complements is employed as a measure of fuzziness, an
interpretation of the approach employed is that the image is being
segmented into separate regions that individually exhibit the
distinctiveness of each region. This may also provide an approach
to compress the distinctly separate regions by using the redundant
signal information. This may prove useful in a variety of contexts,
such as, where the segmented portions of the image are to be
compressed and separately transmitted across a limited bandwidth
communications channel, for example. It is, likewise, noted that
the approach employed in this particular embodiment does not have
difficulty dealing with blurring or with discontinuities in the
histogram generated from the image. For example, the histogram in
FIG. 3 shows such a discontinuity. Therefore, this particular
embodiment has advantages over alternative approaches of image
segmentation.
It will, of course, be appreciated, as previously indicated, that
the invention is not limited in scope to the previously described
embodiment. For example, alternatively, a computing platform, such
as, for example, a personal computer, including a desktop or laptop
computer, or a server, may include hardware and/or software and/or
firmware that provides the capability for the platform to perform
image segmentation in accordance with the present invention, such
as, for example, by employing the technique previously described
and illustrated. Likewise, in an another alternative embodiment, a
storage medium, such as a compact disk, a hard disk drive, or a
floppy disk, for example, may have stored thereon instructions
that, when executed by a computing platform, result in image
segmentation being performed in accordance with the present
invention.
While certain features of the invention have been illustrated and
described herein, many modifications, substitutions, changes and
equivalents will now occur to those skilled in the art. It is,
therefore, to be understood that the appended claims are intended
to cover all such modifications and changes as fall within the true
spirit of the invention.
* * * * *